1. Field of the Invention
This invention relates to a method of measuring the geometric distortion of an optical imaging system.
2. Description of Related Art
In any application where a lens is used to image a scene onto a planar surface such as a ground glass screen or onto a photosensitive material such as film or a television camera vidicon, a certain amount of geometric distortion will exist. This distortion is not a problem in most applications where the viewed image is accepted subjectively by the viewer. Even when distortion is severe, as in wide angle or fish eye photographs, the viewer can adjust, and may even accept the distortion as desirable. However, in applications where the accuracy of the image can affect the accuracy of a process, such as in vision systems for manufacturing, photolithography, and numerical machining controls, distortion can create excessive inaccuracies or out of tolerance measurements.
A useful definition of the distortion of an optical imaging system is the departure of the system from ideal behavior. Ideally, a lens system should produce a unique image point corresponding to each object point, and every straight line in the object space should have a corresponding straight line image in the image space. When the conditions for such a colinear transformation are not met, the departures from that ideal behavior are termed aberrations.
Conventionally, to calculate this distortion requires a complete knowledge of the imaging system, i.e., the exact characteristics of the lens such as its modulation transfer function (MTF), focal length, and its alignment with the photosensitive image plane. These characteristics are difficult to quantify and when the lens and/or camera are changed, one has to repeat the necessary measurement or calculation steps in order to obtain a new measure of the system distortion. Such repetition is both costly and time consuming.
The normal approach is to use the longest possible focal length with the best known high quality lens and the resultant system performance using a grid pattern to measure the distortion. This technique is not only time consuming, but also inadequate for many applications. In many instances, quantitative distortion measurements are simply not readily obtainable and the analysis leaves too many questions relating to actual lens characteristics. It is generally impractical to scan the distorted grid pattern image in order to obtain a quantitative two-dimensional map of the distortions over the entire image, except for relatively large scale aberrations, because the variables required for the analysis cannot be determined with sufficient accuracy, and thus full automation of the distortion measurement process has not been adopted.
An improvement to the method of directly analyzing a grid pattern viewed through the imaging system is to view the grid pattern image through another grid pattern placed downstream of the lens being analyzed in order to obtain a Moire pattern. The examination of the lens can be carried out using an analysis of the Moire pattern observed.
The Moire pattern contains fringes which are readily identifiable even where the line spacing is too small to be detected. If the repeat spacing of one grating differs even slightly from that of the other, a beat pattern will be observed when the lines of the two figures are crossed at zero angle. The beat spacing is inversely proportional to the difference in spacings of the two gratings.
While this type of conventional Moire pattern analysis has the effect of amplifying small aberrations, making them easier to detect, the use of a second discrete grating or reference prevents one from measuring overall imaging system distortion. If the actual image plane is not used as the detection plane, inaccuracies will be contributed by the positioning of the detection plane relative to the imaging system or element being analyzed. Despite the improved accuracy, conventional Moire pattern distortion measurement techniques continue to be, in practice, both costly and time consuming, and do not readily lend itself to automated quantitative analysis.